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A-nice-question-lt-3-If-a-quadratic-equation-1-q-p-2-2-x-2-p-1-q-x-q-q-1-p-2-2-0-has-equal-roots-prove-that-p-2-4q-

Question Number 113684 by ZiYangLee last updated on 14/Sep/20 $$\mathrm{A}\:\mathrm{nice}\:\mathrm{question}\:<\mathrm{3} \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{equation}\: \\ $$$$\left(\mathrm{1}−{q}+\frac{{p}^{\mathrm{2}} }{\mathrm{2}}\right){x}^{\mathrm{2}} +{p}\left(\mathrm{1}+{q}\right){x}+{q}\left({q}−\mathrm{1}\right)+\frac{{p}^{\mathrm{2}} }{\mathrm{2}}=\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{equal}\:\mathrm{roots},\:\mathrm{prove}\:\mathrm{that}\:{p}^{\mathrm{2}} =\mathrm{4}{q} \\ $$ Commented…

In-ABC-BC-5cm-AC-4cm-cos-A-B-31-32-Find-the-area-of-ABC-

Question Number 113667 by ZiYangLee last updated on 14/Sep/20 $$\mathrm{In}\:\bigtriangleup\mathrm{ABC},\:\mathrm{BC}=\mathrm{5cm}\:\mathrm{AC}=\mathrm{4cm} \\ $$$$\mathrm{cos}\left(\mathrm{A}−\mathrm{B}\right)=\frac{\mathrm{31}}{\mathrm{32}}\:\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\bigtriangleup\mathrm{ABC}. \\ $$ Answered by som(math1967) last updated on 14/Sep/20 $$\mathrm{tan}^{\mathrm{2}} \frac{\mathrm{A}−\mathrm{B}}{\mathrm{2}}=\frac{\mathrm{1}−\mathrm{cos}\left(\mathrm{A}−\mathrm{B}\right)}{\mathrm{1}+\mathrm{cos}\left(\mathrm{A}−\mathrm{B}\right)}…

Question-113668

Question Number 113668 by mohammad17 last updated on 14/Sep/20 Answered by john santu last updated on 14/Sep/20 $${If}\:\int_{−\mathrm{2}} ^{\mathrm{6}} \left({f}\left({x}\right)+\mathrm{3}\right){dx}\:=\:\mathrm{32}\:\rightarrow\int_{−\mathrm{2}} ^{\mathrm{6}} {f}\left({x}\right){dx}+\mathrm{3}\left(\mathrm{8}\right)=\mathrm{32} \\ $$$$\:\int_{−\mathrm{2}} ^{\mathrm{6}}…

46-2-60-hi-sir-plx-help-me-

Question Number 48111 by ggny last updated on 19/Nov/18 $$\left(−\mathrm{46}−×\right)/\left(−\mathrm{2}\right)=\mathrm{60}\:\: \\ $$$${hi}\:{sir}\:{plx}\:{help}\:{me} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 19/Nov/18 $$\frac{−\mathrm{46}−{x}}{−\mathrm{2}}=\mathrm{60} \\ $$$$−\mathrm{46}−{x}=−\mathrm{120} \\…

Prove-that-there-exists-M-gt-0-such-that-for-any-positive-integers-n-we-have-1-2-n-1-M-

Question Number 113641 by ZiYangLee last updated on 14/Sep/20 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exists}\:{M}>\mathrm{0}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{for}\:\mathrm{any}\:\mathrm{positive}\:\mathrm{integers}\:{n},\:\mathrm{we}\:\mathrm{have} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{2}+\sqrt{…+\sqrt{{n}+\mathrm{1}}}}}\leqslant{M} \\ $$ Commented by mr W last updated on 14/Sep/20 $${A}_{{n}}…